Golf ball trajectory computing system and method of computing trajectory of golf ball

ABSTRACT

A trajectory of a struck golf ball from when the golf ball is struck until the golf ball lands is computed by a golf ball trajectory computing system. The system comprises: an initial trajectory measuring portions that measures an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after impact thereof; a carry distance measuring portion that measures a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; a duration-of-flight measuring portion that measures a duration of flight of the golf ball from impact thereof until the golf ball lands; and a computing portions that computes a trajectory of the golf ball based on the measured initial velocity, the measured launch angle, and the measured backspin of the golf ball immediately after impact, and the carry distance and the duration of flight of the golf ball.

INCORPORATION BY REFERENCE

This application claims priority on Japanese patent application No.2004-095488, the entire contents of which are hereby incorporated by reference.

BACKGROUND OF THE INVENTION

The present invention relates to a golf ball trajectory computing system and a method of computing the trajectory of a golf ball in order to easily find the trajectory of a golf ball from when the golf ball is struck until the golf ball lands.

Methods of measuring the trajectory of a golf ball in real time, in which trajectory measurement states can be monitored, have been proposed (refer to JP 6-323852 A, for example).

JP 6-323852 A discloses a conventional method of measuring the trajectory of a golf ball. A measuring system thereof is configured by a CCD camera with a shutter, a video memory, a video monitor, and a controller unit. The CCD camera photographs a golf ball. Resultant images undergo high speed comparison processing at a pixel by pixel level, and only portions where changes are present are stored in the video memory and displayed. A composite image is thus displayed on the video monitor and recorded. The measuring system thus measures the trajectory of the golf ball.

Only moving portions are extracted with the convention measurement method, without any influence of the brightness of the golf ball, the background, or the like. Accordingly, the trajectory of the golf ball can be clearly measured.

There is a problem, however, with the method of measuring the trajectory of a golf ball disclosed in JP 6-323852 A in that, when measuring the trajectory of the golf ball, measurements must be made with the entire golf ball trajectory in a visible state. Golf balls are small, and the golf ball carry distance exceeds 100 m. Consequently, there is a problem in that the trajectory measurement precision decreases when the entire trajectory is put into frame by using one CCD camera.

Further, terms of art such as high trajectory, mid trajectory, and low trajectory are currently used in order to express characteristics of golf ball trajectories. However, the basis for using such terms is unclear. The terms high trajectory, mid trajectory, and low trajectory are unable to accurately describe the characteristics of golf ball trajectories, and thus are not suited thereto.

SUMMARY OF THE INVENTION

The present invention has been made to solve problems like those described above based on conventional techniques. An object of the present invention is to provide a golf ball trajectory computing system, and a method of computing a trajectory of a golf ball, in which the trajectory of a struck golf ball from when the golf ball is struck until the golf ball lands can easily be found.

Further, another object of the present invention is to provide a golf ball trajectory computing system, and a method of computing a trajectory of a golf ball, capable of correctly evaluating the trajectory of a golf ball.

In order to achieve the above objects, the present invention provides a golf ball trajectory computing system that computes a trajectory of a struck golf ball from when the golf ball is struck until the golf ball lands, comprising: initial trajectory measuring portion that measures an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after impact thereof; carry distance measuring portion that measures a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; duration-of-flight measuring portion that measures a duration of flight of the golf ball from impact thereof until the golf ball lands; and computing portion that computes a trajectory of the golf ball based on the measured initial velocity, the measured launch angle, and the measured backspin of the golf ball immediately after impact, and the carry distance and the duration of flight of the golf ball.

In the system, it is preferable that the computing portion computes an average drag coefficient and an average lift coefficient for the golf ball during flight from the initial velocity of the golf ball, the launch angle, and the backspin rate immediately after impact, and from the carry distance and the duration of flight, and computes the trajectory of the golf ball using the computed average drag coefficient and the computed average lift coefficient.

It is also preferable that the computing portion computes the trajectory of the golf ball using equations of motion of the golf ball, and sets an average drag coefficient and an average lift coefficient so that the carry distance and the duration of flight computed by using the equations of motion of the golf ball match the carry distance measured by the carry distance measuring portion and the duration of flight measured by the duration-of-flight measuring portion, respectively, within a predetermined error range.

The present invention also provides a method of computing a trajectory of a golf ball, comprising: measuring an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after the golf ball is struck; measuring a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; measuring the duration of flight of the golf ball from impact thereof until the golf ball lands; and computing the trajectory of the golf ball based on the initial velocity, the launch angle, and the backspin rate of the golf ball immediately after impact thereof, based on the carry distance and the duration of flight.

In the method, it is preferable that the computing of the trajectory of the golf ball further comprises computing an average drag coefficient and an average lift coefficient of the golf ball during flight from the initial velocity, the launch angle, and the backspin rate of the golf ball immediately after impact thereof, and from the carry distance and the duration of flight, and computing the trajectory of the golf ball using the computed average drag coefficient and the computed average lift coefficient.

More preferably, the computing of the trajectory of the golf ball further comprises: setting an initial value of the average drag coefficient and an initial value of the average lift coefficient of the golf ball during flight; finding a computed value of the carry distance and a computed value of the duration of flight of the golf ball based on the initial value of the average drag coefficient and the initial value of the average lift coefficient; comparing the computed value of the carry distance and the computed value of the duration of flight with the measured value of the carry distance and the measured value of the duration of flight, respectively; and based on results of the comparing, computing an average drag coefficient and an average lift coefficient of the golf ball during flight, so that the computed value of the carry distance and the computed value of the duration of flight of the golf ball fall within a predetermined error range with respect to the measured value of the carry distance and the measured value of the duration of flight, by adjusting at least one of the initial value of the average drag coefficient and the initial value of the average lift coefficient.

The golf ball trajectory computing system according to the present invention includes: initial trajectory measuring portion that measures an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after impact thereof; carry distance measuring portion that measures a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; duration-of-flight measuring portion that measures a duration of flight of the golf ball from impact thereof until the golf ball lands; and computing portion that computes a trajectory of the golf ball based on the measured initial velocity, launch angle, and amount of backspin of the golf ball immediately after impact, and the carry distance and the duration of flight of the golf ball. Only initial trajectory characteristic values, the carry distance, and the duration of flight are measured. The golf ball trajectory computing system can thus compute the trajectory of a golf ball with ease and high precision without using large scale equipment or multiple measuring devices.

The method of computing a trajectory of a golf ball according to the present invention is capable of computing the trajectory of the struck golf ball by measuring an initial velocity, a launch angle, a backspin rate, a carry distance, and a duration of flight thereof. Large scale equipment and multiple measuring devices are thus unnecessary, and the trajectory of a golf ball can be computed with ease and high precision.

In addition, an average drag coefficient and an average lift coefficient may both be computed with the golf ball trajectory computing system and a method of computing the trajectory of a golf ball according to the present invention. The characteristics of the struck golf ball can thus be expressed by values having a scientific basis.

BRIEF DESCRIPTION OF THE DRAWINGS In the accompanying drawings:

FIG. 1 is a schematic view that shows a golf ball trajectory computing system according to an embodiment of the present invention;

FIG. 2 is a side view that schematically shows an initial trajectory measuring apparatus of the present invention;

FIG. 3 is a schematic view that shows an example of an image obtained by the initial trajectory measuring apparatus of this embodiment;

FIG. 4 is a flowchart that shows a method of computing the trajectory of a golf ball of this embodiment;

FIG. 5 is a flowchart that explains a method of measuring initial trajectory characteristic values of a golf ball;

FIGS. 6A to 6C are timing charts that explain an example of signal timing for controlling the operation of a camera of the initial trajectory measuring apparatus of this embodiment;

FIGS. 7A to 7C are timing charts that explain another example of signal timing for controlling the operation of the camera of the initial trajectory measuring apparatus of this embodiment; and

FIG. 8 is a graph that shows results of computing the trajectory of a golf ball in a first embodiment, with striking height shown on the vertical axis and carry distance shown on the horizontal axis.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A golf ball trajectory computing system and a method of computing the trajectory of a golf ball of the present invention are explained in detail below based on preferred embodiments shown in the appended drawings.

FIG. 1 is a schematic view that shows a golf ball trajectory computing system according to an embodiment of the present invention.

A trajectory computing system 100 for a golf ball 8 of this embodiment is explained by taking an example of a golfer 4 hitting the golf ball 8. However, the present invention is not limited to this embodiment, and a striking robot or a ball ejecting apparatus may be used as a substitute for the golfer 4.

The trajectory computing system (hereinafter referred to simply as a computing system) 100 for the golf ball 8 shown in FIG. 1 has an initial trajectory measuring apparatus 2, a carry distance measuring apparatus 3, and a duration-of-flight measuring apparatus 5. A computing device of the initial trajectory computing apparatus 2 functions as computing portion for computing the trajectory of the golf ball according to the present invention. Reference numeral 4 shown in FIG. 1 denotes the golfer, and reference numeral 6 denotes a golf club. Reference numeral 8 denotes a golf ball, and symbol b denotes the trajectory of the golf ball 8.

The principles involved in measuring the trajectory of a golf ball in the present invention are explained below.

Referring to FIG. 1, a drag force D, a lift force L, and a weight force mg act on the golf ball 8 in flight. Eq. (1) below shows equations of motion for the golf ball in a horizontal (x) direction at this point. Further, Eq. (2) below shows equations of motion for the golf ball 8 in a vertical (y) direction.

It should be noted that symbol m in Eq. (1) and Eq. (2) denotes the mass of the golf ball, while symbol θ denotes a flying angle or a launch angle. The flying angle (launch angle) θ is expressed by Eq. 3 below.

Further, the drag force D in Eq. 1 and Eq. 2 is expressed by Eq. 4 below, and the lift force L in Eq. 1 and Eq. 2 is expressed by Eq. 5 below. Symbol U in Eq. 4 and Eq. 5 denotes the golf ball velocity, and the golf ball velocity U is expressed by Eq. 6 below. In addition, symbol C_(D) in Eq. 4 denotes a drag coefficient, symbol C_(L) denotes a lift coefficient, and symbol ρ denotes the density of air. The density of air at a temperature of 20° C. and an atmospheric pressure of 1 (1.013 kPa) is used as the air density ρ. $\begin{matrix} {{m\frac{\mathbb{d}^{2}x}{\mathbb{d}t^{2}}} = {{{- {D(t)}}\cos\quad{\theta(t)}} - {{L(t)}\sin\quad{\theta(t)}}}} & \left( {{Eq}.\quad 1} \right) \\ {{m\frac{\mathbb{d}^{2}y}{\mathbb{d}t^{2}}} = {{{- {D(t)}}\sin\quad{\theta(t)}} + {{L(t)}\cos\quad{\theta(t)}} - {mg}}} & \left( {{Eq}.\quad 2} \right) \\ {\theta = {\tan^{- 1}\frac{\left( \frac{\mathbb{d}y}{\mathbb{d}t} \right)}{\left( \frac{\mathbb{d}x}{\mathbb{d}t} \right)}}} & \left( {{Eq}.\quad 3} \right) \\ {D = {C_{D}A\frac{\rho\quad U^{2}(t)}{2}}} & \left( {{Eq}.\quad 4} \right) \\ {L = {C_{L}A\frac{\rho\quad U^{2}(t)}{2}}} & \left( {{Eq}.\quad 5} \right) \\ {U = \sqrt{\left( \frac{\mathbb{d}x}{\mathbb{d}t} \right)^{2} + \left( \frac{\mathbb{d}y}{\mathbb{d}t} \right)^{2}}} & \left( {{Eq}.\quad 6} \right) \end{matrix}$

As described hereinafter, in this embodiment the initial velocity of the golf ball 8 immediately after impact, the launch angle of the golf ball immediately after impact, the backspin rate of the golf ball 8 immediately after impact (hereinafter the initial velocity of the golf ball 8 immediately after impact, the launch angle of the golf ball 8 immediately after impact, and the backspin rate of the golf ball 8 immediately after impact are referred to collectively as initial trajectory characteristic values), the carry distance of the golf ball 8, and the duration of flight of the golf ball 8 are measured.

An average drag coefficient for the golf ball 8 during flight and an average lift coefficient for the golf ball 8 during flight are then computed based on the measurement results using Eqs. 1 to 6, and the trajectory of the golf ball 8 is then computed. The computations are performed so that deviations between the computed and measured carry distance of the golf ball 8 and the computed and measured duration of flight of the golf ball 8 each fall within a predetermined error range.

The drag coefficient of the golf ball 8 during flight and the lift coefficient of the golf ball 8 during flight each change depending upon factors such as the velocity of the golf ball 8 and the backspin rate of the golf ball 8. In this embodiment, however, the drag coefficient C_(D) and the lift coefficient C_(L) from impact until landing are treated as an average drag coefficient and an average lift coefficient, respectively, having constant values that do not change. Further, a projection area A of the golf ball 8 and the air density ρ are also taken as being constant.

The trajectory of the golf ball 8 can thus be computed in this embodiment by measuring the initial trajectory characteristic values, the carry distance, and the duration of flight. The inventors of the present invention discovered that although it is possible to compute the trajectory of the golf ball 8 by making extensive calculations through sequential computation of Eqs. 1 to 4, the trajectory of the golf ball 8 computed according to the present invention falls within a sufficient error range with respect to actual measurement results. The trajectory of the golf ball 8 can thus be computed with ease and high precision in the present invention, without making extensive calculations.

The initial trajectory measuring apparatus 2 that measures the initial velocity of the golf ball 8 immediately after impact, the launch angle of the golf ball 8 immediately after impact, and the backspin rate of the golf ball 8 immediately after impact, the carry distance measuring apparatus 3 that measures the carry distance of the golf ball 8, and the duration-of-flight measuring apparatus 5 that measures the duration of flight of the golf ball 8 in this embodiment are explained below.

FIG. 2 is a side view that schematically shows an initial trajectory measuring apparatus of the present invention.

Referring to FIG. 2, the initial trajectory measuring apparatus 2 for the golf ball 8 measures initial trajectory characteristic values of the golf ball 8 (initial velocity, launch angle, and backspin rate) when the golfer 4 test-hits the golf ball 8 using the golf club 6, for example.

The initial trajectory measuring apparatus 2 includes two mirrors 10 and 12 on opposite sides of the golfer 4, sandwiching the golf ball 8, which is an object to be photographed. The two mirrors 10 and 12 reflect images of the golf ball 8 that has been struck from a tee, on which the golf ball 8 is placed before being struck. The initial trajectory measuring apparatus 2 also includes a half mirror 14. Two images of the golf ball immediately after being struck that are reflected by the two mirrors 10 and 12, respectively, are projected onto different surfaces of the half mirror 14. The image projected from the mirror 10 is reflected by the half mirror 14, while the image projected from the mirror 12 is transmitted through the half mirror 14. The initial trajectory measuring apparatus 2 also includes a high resolution CCD camera 16 that photographs the golf ball image that has passed through the half mirror 14, together with the image of the golf ball that has been reflected by the half mirror 14. The initial trajectory measuring apparatus 2 also includes an initial trajectory characteristic computing portion 17 that computes the initial trajectory characteristic values of the golf ball 8 based on the images of the golf ball 8 photographed by the CCD camera 16.

The mirrors 10 and 12 are disposed in the periphery of an assumed trajectory path immediately after the golf ball 8 is struck, at approximately equal distances from the golf ball 8 immediately after the golf ball 8 is struck, so as to reflect images of the golf ball from two different directions.

The half mirror 14 is an optical member having a boundary surface that at least transmits an image projected from one side thereof, and at least reflects an image that is projected from another side thereof. The half mirror 14 is disposed on a plane of symmetry 18 in a position substantially symmetrical between the locations of the mirrors 10 and 12, so that the boundary surface of the half mirror 14 becomes parallel with the plane of symmetry 18. In other words, the inclination angles of the reflective surfaces of the mirrors 10 and 12 with respect to the surface of the half mirror 14 or the plane of symmetry 18 are set to have opposite signs, while having equal absolute values (angles +α° and −α° in FIG. 2).

Further, although the initial trajectory measuring apparatus 2 for the golf ball 8 photographs images of the golf ball 8 from two different directions immediately after the golf ball 8 is struck, by making minute adjustments in the positions of the mirrors 10 and 12, the angles at which the two images of the golf ball are projected on the half mirror 14 can be made substantially equal. In addition, by making another minute adjustments in the positions of the mirrors 10 and 12 so that the golf ball images are as close to each other as possible without overlapping, golf ball images are formed close together. The CCD camera can thus photograph the close together golf ball images as one image. A controller device 22 is provided connected to the CCD camera 16. The controller device 22 performs control to automatically open and close an electronic shutter so that the CCD camera 16 can perform photography at a predetermined timing. The field of view of a region photographed by the CCD camera 16 can thus be made narrower, and the images of the golf ball 8 can be photographed with high precision, by making the golf ball images, seen from two different directions approach each other using the half mirror 14. Further, the two images of the golf ball tend to not overlap, thus making it possible to perform later image processing and make later measurements of the initial trajectory characteristic values.

An arbitrary optical camera can also be used instead of the CCD camera 16. However, it is preferable to use the CCD camera 16, which outputs digitized images, in order to easily detect the position of the golf ball 8 when measuring initial trajectory characteristic values such as the initial velocity and the launch angle of the golf ball 8, rotational angular velocities such as a backspin rate and a side spin rate, and rotation direction, as described hereinafter. This is because the images of the golf ball 8 can be quickly detected by performing image processing on the photographed images of the golf ball 8. Further, the initial trajectory measuring apparatus 2 for the golf ball 8 of this embodiment can be made portable by being received in a case 20 in which the components are arranged and fixed and which has a surface covered with a transparent member through which the two images of the object to be photographed that are projected by the two mirrors 10 and 12, and can be easily moved and installed in any location. In addition, a strobe apparatus that illuminates the golf ball 8 during photography thereof, or depending upon the circumstances, an apparatus that emits light such as natural light or artificial light having sufficient brightness may of course also be used.

When measuring the initial trajectory characteristic values of the golf ball 8 with the initial trajectory measuring apparatus 2 for the golf ball 8 thus configured, images of the golf ball 8 struck and flying immediately after impact are photographed as one planar image by strobe light emitted two times at points in time with a predetermined interval of time therebetween. As becomes clear when referring to FIG. 2, the images of the golf ball 8 that are reflected by the mirror 10, and then re-reflected by the half mirror 14 and projected to the CCD camera 16 (hereinafter called an upper side images), are set to appear in an upper side of the image photographed by the CCD camera 16. The images of the golf ball 8 that are reflected by the mirror 12, and then transmitted through the half mirror 14 and projected to the CCD camera 16 (hereinafter called a lower side images), are set to appear in a lower side of the image photographed by the CCD camera 16. Referring to FIG. 3, four golf ball images 32, 34, 36, and 38 are recorded within one planar image 30.

FIG. 3 is a schematic view that shows an example of an image obtained by using the initial trajectory measuring apparatus of this embodiment.

The golf ball images 32 and 34 are upper side images in this embodiment, and the golf ball images 36 and 38 are lower side images, as described above. Further, the strobe light is emitted two times at points in time with a predetermined interval of time therebetween. Accordingly, the golf ball images 34 and 36 are photographed using the first strobe illumination light, while the golf ball images 32 and 38 are photographed using the second strobe illumination light. The two strobe illumination lights are emitted after a shutter of the CCD camera 16 is opened following a predetermined time delay from a point where a trigger signal is generated by the swinging golf club passing immediately prior to impacting the golf ball 8. Images of the golf ball 8 are photographed when the two strobe illumination lights are emitted.

The golf ball images 32 and 34 as the upper side images and the golf ball images 36 and 38 as the lower side images are photographed and combined into four images on the planar image 30. The golf ball images 34 and 36 are photographed first, while the golf ball images 32 and 38 are photographed after the predetermined interval of time has elapsed.

A black circle or cross shaped mark is disposed on the golf ball 8 as a point of specification in order to allow the initial trajectory measuring apparatus 2 to measure the rotational angular velocity and rotation direction of the struck golf ball 8, such as the backspin rate and the side spin rate. The rotational angular velocity and the rotation direction of the golf ball 8 are measured according to the movement distance and movement direction of the mark position on the surface of the golf ball 8. Marking images 32 a, 34 a, 36 a, and 38 a are shown as black circles in inner portions of the golf ball images 32, 34, 36, and 38, respectively, in the planar image 30 of FIG. 3. In the upper side images, the marking moves and rotates on the surface of the golf ball 8 from the marking image 32 a to the marking image 34 a. In the lower side images, the marking moves and rotates on the surface of the golf ball 8 from the marking image 36 a to the marking image 38 a.

It should be noted that there are no limitations placed on the planar image 30 where to arrange the four golf ball images 32, 34, 36, and 38 in the planar image 30, photographed by the CCD camera 16 using the strobe illumination light emitted at points in time with a predetermined interval of time therebetween. An image may also be used in which the golf ball images 32, 34, 36, and 38 are photographed by opening the shutter of the CCD camera 16 two times, with the predetermined interval of time therebetween, resulting in multiple exposures. In addition, the shutter may also be opened only for the predetermined interval of time, and a residual image of the golf ball 8 in the direction of travel may be obtained. Images of the golf ball 8 at both ends of the residual image may be used as the four golf ball images 32, 34, 36, and 38. Further, images may also be extracted from images photographed by a high speed video camera with the same predetermined interval of time therebetween. Images at both ends of the extracted images may be used as the four golf ball images 32, 34, 36, and 38.

The planar image 30 photographed by the CCD camera 16 is sent to the initial trajectory characteristic value computing portion 17.

The projection angle of the two images of the golf ball that are projected onto the half mirror 14 are thus made to substantially coincide, and moreover, the images of the golf ball 8 are arranged close each other. In addition, the angles of incline of the reflecting surfaces of the mirrors 10 and 12 with respect to the half mirror 14 have mutually opposite signs and substantially equal absolute values. Accordingly, the path lengths of the golf ball images from the golf ball 8 being photographed, which are reflected by the mirror 10 or the mirror 12 and reacht the CCD camera 16, become substantially equal. One of the golf ball images does not become out of focus unlike conventional apparatuses.

Meanwhile, the initial trajectory characteristic computing portion 17 has an image reading device 40, a position computing device 42, a computing device 44, a memory device 45, and a CPU 46.

The image reading device 40 reads the planar image 30 photographed by the CCD camera 16 as digital data, and performs image processing to delete unnecessary image portions, such as the environment in the periphery of the golf ball 8. The image reading device 40 then performs image processing on an image of the external shape of the golf ball 8, and computes the respective center-of-mass positions of the images 32, 34, 36, and 38 of the golf ball 8. The image reading device 40 next performs image processing on the marking images 32 a, 34 a, 36 a, and 38 a formed on the golf ball 8, and computes the respective center positions of the marking images 32 a, 34 a, 36 a, and 38 a. Computational results are output to the position measuring device 42.

The position measuring device 42 computes vertical movement and horizontal movement of the actual movement path of the golf ball 8 when data on the center-of-mass positions of the golf ball images 32, 34, 36, and 38, and data on the center positions of the marking images 32 a, 34 a, 36 a, and 38 a are input.

Referring to FIG. 1, the two mirrors 10 and 12 are inclined at predetermined angles. Accordingly, the coordinates of the center-of-mass positions of the golf ball images 32, 34, 36, and 38, and the coordinates of the center positions of the marking images 32 a, 34 a, 36 a, and 38 a in the images reflected by the mirrors 10 and 12 and photographed as the planar image 30 include an additional vertical component and an additional horizontal component depending upon the inclination angle of the mirrors 10 and 12. The numerical values of the coordinates of the center-of-mass positions of the golf ball images 32, 34, 36, and 38, and the numerical values of the coordinates of the center positions of the marking images 32 a, 34 a, 36 a, and 38 a are therefore decomposed into an actual vertical component and an actual horizontal component according to the positional arrangement of the mirrors 10 and 12. The coordinates of the center-of-mass position of the golf ball 8 at the initial strobe emission point, and the coordinates of the center position of the marking with respect to the center-of-mass position of the golf ball 8 are then measured. In addition, the coordinates of the center-of-mass position of the golf ball 8 at the second strobe emission point, and the coordinates of the center position of the marking with respect to the center-of-mass position are also measured. Each of the measured coordinate values is sent to the computing device 44.

The computing device 44 computes the initial velocity and the launch angle of the golf ball 8 by finding the movement distance and the movement direction of the center-of-mass position of the golf ball 8 from the coordinates of 6the center-of-mass positions of the golf ball 8 and the center positions of the marking at the initial strobe emission point and the second strobe emission point. The computing device 44 computes the rotational angular velocity and the rotation direction of the golf ball 8 by finding the movement distance and the movement direction of the center position of the marking, and then computes the backspin rate and the side spin rate of the golf ball 8.

Further, the memory device 45 is connected to the computing device 44. The memory device 45 is also connected to the carry distance measuring apparatus 3 and the duration-of-flight measuring apparatus 5, and stores the carry distance and the duration of flight associated with the initial trajectory characteristic values. A trajectory b of the golf ball 8, the average value of the drag coefficient, and the average value of the lift coefficient are computed by the computing device 44 as described hereinafter using Eqs. 1 to 4, the carry distance, the duration of flight, and the initial trajectory characteristic values, and the trajectory of the golf ball is further computed. In other words, the computing device 44 functions as computing portion for computing the trajectory of the golf ball in the present invention.

It should be noted that the memory device 45 has memory elements such as DRAM.

Further, the carry distance measuring apparatus 3 for the golf ball 8 shown in FIG. 1 measures the carry distance from an impact point a, at which the golf ball 8 is teed up, to a landing point c where the golf ball 8 lands after being struck. There are no particular limitations placed on the carry distance measuring apparatus 3. For example, a measuring tape, a distance measuring apparatus that utilizes the global positioning system (GPS) may be used, and a distance measuring apparatus that optical equipment may also be used. It should be noted that the term carry distance as used in this embodiment does not include run after the golf ball 8 lands.

The duration-of-flight measuring apparatus 5 for the golf ball 8 measures an amount of time required between the striking point a and the landing point c. There are no particular limitations placed on the duration-of-flight measuring apparatus 5. For example, the duration-of-flight measuring apparatus 5 may be a timer that is connected to the initial trajectory measuring apparatus 2 and that takes measurements in synchronization with the initial trajectory measuring apparatus 2.

In this embodiment the initial trajectory characteristic values, the carry distance, and the duration of flight are measured by the initial trajectory measuring apparatus 2, the carry distance measuring apparatus 3, and the duration-of-flight measuring apparatus 5, respectively. The computing device 44 of the initial trajectory measuring apparatus 2 then computes the trajectory b of the golf ball 8.

Further, there are no particular limitations placed on the units of measurement used for the initial velocity, the launch angle, the backspin rate, the carry distance, and the duration of flight.

The initial velocity expresses a movement distance per unit time. There are no particular limitations placed on the unit of measurement used for the initial velocity, and m/second may be used, for example.

Further, the launch angle expresses an angle. There are no particular limitations placed on the unit of measurement used for the launch angle, and degrees (°) may be used, for example.

Furthermore, the backspin rate expresses rotations per unit time. There are no particular limitations placed on the unit of measurement used for the backspin rate, and revolutions per minute (rpm) may be used, for example.

The carry distance expresses a distance. There are no particular limitations placed on the unit of measurement used for the carry distance, and yards may be used, for example.

Further, the duration of flight expresses an amount of time. There are no particular limitations placed on the unit of measurement used for the duration of flight, and seconds may be used, for example.

A method of computing the trajectory of a golf ball of the present invention is explained next.

FIG. 4 is a flowchart that shows a method of computing the trajectory of a golf ball of this embodiment.

First, the initial trajectory characteristic values, the carry distance, and the duration of flight are measured when a teed up golf ball is struck by a golfer (step S1).

A method of measuring the initial trajectory characteristic values in step S1 is explained in detail below.

FIG. 5 is a flowchart that explains a method of measuring the initial trajectory characteristic values of the golf ball 8.

First, the golfer 4 or a swing robot (not shown) begins swinging the golf club 6 (step S100).

FIGS. 6A to 6C are timing charts that explain an example of signal timing that controls operation of the camera of the initial trajectory measuring apparatus 2 in this embodiment.

Next, when the golf club head of the golf club 6 passes through a detection position of a golf club head detecting device (not shown) disposed in a region immediately before impact, the a trigger signal like that shown in FIG. 6A is generated in the golf club head detecting device (step S102). The trigger signal is sent from the golf club head detecting device to the controller device 22.

The controller device 22 generates a camera operation signal like that shown in FIG. 6B so that the electronic shutter of the CCD camera 16 opens T₁ seconds after the rise of the trigger signal, and sends the camera operation signal to the CCD camera 16. The camera operation signal causes the electronic shutter to open for T₂ seconds (step S104)

At the same time, the controller unit 22 sends a strob illumination signal like that shown in FIG. 6C to a strobe (not shown). The strobe emits light two times at the time interval of T₃ seconds during the T₂ seconds during which the electronic shutter is open (step S106), thus illuminating the golf ball 8. The initial trajectory of the golf ball 8 immediately after being struck is photographed by the two emissions of light from the strobe at the time interval of T₃ seconds (step S108), thus obtaining the one planar image 30 from the golf ball images at the beginning and the end of the T₃ second period of time.

It should be noted that, as discussed hereinafter, a high speed camera that performs photography by opening a shutter two or more times when photographing the golf ball, thus photographing with multiple exposures, may also be used to obtain the one planar image 30.

At the same time, a head speed measuring device (not shown) measures the head speed of the golf club 6 (step S110). The head speed measuring device may be a device that is separate from the initial trajectory measuring apparatus 2 for the golf ball 8 of this embodiment. Alternatively, two sensors may be disposed in the golf club head detecting device at a predetermined spacing, and the golf club head speed may be measured by using a time interval between detection of the golf club head by the two sensors.

The planar image obtained in step S108 in which the initial trajectory of the golf ball 8 is photographed is then displayed in a display device 48 along with data such as the head speed of the golf club head obtained in step S110 (step S112). The image reading device 40 reads in data as digital data and removes unnecessary image portions such as the periphery environment, and then performs image processing on the outer diameter images of the golf ball 8 (step S114). The image reading device 40 then computes the center-of-mass positions of the golf ball images 32, 34, 36, and 38 (step S116). At the same time, the image reading device 40 performs image processing on the images 32 a, 34 a, 36 a, and 38 a of the marking provided on the golf ball 8 (step S118), and computes the center positions of the marking images 32 a, 34 a, 36 a and 38 a (step S120).

The position measuring device 42 then measures the center-of-mass positions (step S122). The computing device 44 computes the initial trajectory characteristic values of the golf ball 8. The computing device 44 computes the initial velocity and the launch angle of the golf ball 8 from the movement distance and the movement direction of the center-of-mass position of the golf ball 8, and computes the backspin rate of the golf ball 8 from the movement distance and the movement direction of the center position of the marking on the golf ball 8 (step S124).

Next, the initial trajectory characteristic values of the golf ball 8 are stored in the memory device 45 at a point where measurement of the initial trajectory characteristic values is complete (step S128), thus completing measurements of the golf ball 8 made by the initial trajectory measuring apparatus 2. It should be noted that the carry distance measuring apparatus 3 measures the carry distance of the golf ball 8 at this point, and the duration-of-flight measuring apparatus 5 measures the duration of flight of the golf ball 8 at this point. The carry distance and the duration of flight are stored in the memory device 45 in association with the initial trajectory characteristic values. Processing then proceeds to step S2 shown in FIG. 4.

In the measurement method described above, the strobe is made to emit light two times at the time interval of T₃ seconds while the electronic shutter of the CCD camera 16 is open. A high speed camera may also be used, however, as shown in FIGS. 7A to 7C. A camera operation signal (shown in FIG. 7B) may be generated to open a shutter T₁ seconds after the rise of a trigger signal (shown in FIG. 7A), and to again open the shutter after T₃ seconds have elapsed, thus photographing the golf ball image with double exposures. Referring to FIG. 7C, when sufficient light cannot be ensured, a strobe illumination signal may be generated to cause the strobe to emit light for a long period of time covering at least the two times when the shutter opens. Alternatively, a strobe illumination signal may be generated to cause the strobe to flash two times in synchronization with the two shutter openings. On the other hand, when an amount of light sufficient for photography can be ensured by natural light or the like, it is unnecessary to emit light from a strobe or the like. In particular, a sufficient amount of light can be obtained when double exposure photography is performed outdoors, and illumination light from a strobe or the like becomes unnecessary. Photography can thus be performed easily.

Referring to FIG. 4, measured values of the initial trajectory characteristic values, the carry distance H, and the duration of flight T measured in step S1 are given to Eqs. 1 to 4 (step S2).

Initial values for the average drag coefficient C_(Da) and the average lift coefficient C_(La) are then set (step S3).

Eq. 1 and Eq. 2 are solved next, thus computing the carry distance and the duration of flight (step S4).

The difference between the measured value of the carry distance H and the computed value of the carry distance H_(S), and the difference between the measured value of the duration of flight T and the computed value of the duration of flight T_(S) are then found, and a judgement is made as to whether or not the differences are within a predetermined error range (step S5).

In step S5 it is necessary that both the carry distance and the duration-of-flight differences be within permitted error ranges. The permitted error range for the carry distance may be set to 0.5 m, for example, and the permitted error range for the duration of flight may be set to 0.1 second, for example. It should be noted that there are no particular limitations placed on the permitted error ranges. Suitable changes in the values may of course be made depending upon the precision required.

When the differences fall within the permitted error ranges in step S5, the initial values of the average drag coefficient C_(Da) and the initial value of the average lift coefficient C_(La) set in step S3 are set as the average drag coefficient C_(Da) and the average lift coefficient C_(La), respectively.

On the other hand, when one of more of the differences fall outside of the permitted ranges in step S5, at least one of the average drag coefficient C_(Da) and the average lift coefficient C_(La) is set again (step S7).

The average drag coefficient C_(Da) is changed by 0.0001 in step S7, while the average lift coefficient C_(La) is changed by 0.001 in step S7.

The processing then returns to step S4, and the carry distance H_(S) and the duration of flight T_(S) are computed. A difference judgement is then again made in step S5, and processing is repeated until the errors fall within the permitted ranges.

The average drag coefficient C_(Da) and the average lift coefficient C_(La) can thus be found by setting the values of the average drag coefficient C_(Da) and the average lift coefficient C_(La) to values such that the differences between the measured value of the carry distance H and the computed value of the carry distance H_(S), and between the measured value of the duration of flight T and the computed value of the duration of flight T_(S), each fall within the predetermined error range.

The trajectory of the golf ball can be computed based on the average drag coefficient C_(Da) and the average lift coefficient C_(La).

The trajectory thus obtained accurately replicates the trajectory of the actually struck golf ball.

It should be noted that, although at least one of the average drag coefficient C_(Da) and the average lift coefficient C_(La) is set again (adjusted) in this embodiment so that the differences between the measured values and the computed values each fall within the predetermined error range, there are no limitations placed on this method. Ratios of the computed values to the values may also be used. The trajectory of the golf ball can be found with high precision in this embodiment by using the initial trajectory characteristic values, the carry distance, and the duration of flight.

Further, the average drag coefficient C_(Da) of the golf ball during flight and the average lift coefficient C_(La) of the golf ball during flight are computed in this embodiment. It therefore becomes possible to express trajectory characteristics such as how high the golf ball flies based on the golf ball trajectory. The characteristics of commercial golf balls can thus be displayed on packages thereof. It is possible to promote and advertise the characteristics of commercial golf balls using a scientific basis.

The present invention is basically described above.

The golf ball trajectory measuring system and the method of measuring the trajectory of a golf ball according to the present invention are explained in detail above. The present invention is not limited to the embodiments describe above, however. It is of course possible to make a variety of improvements and changes in a scope that does not deviate from the gist of the present invention.

EXAMPLE

Specific examples of the present invention is described below by making a comparison.

In these examples the launch angle is changed using the same golf ball struck by a ball striking machine under conditions of the initial velocity set to 60 m/second and the backspin rate set to 2500 rpm. The carry distance and the duration of flight were then measured at various launch angles. The results are shown in Table 1.

The average drag coefficient C_(Da) and the average lift coefficient C_(La) were computed based on Example 1 shown in Table 1 below. The average drag coefficient C_(Da) was 0.216, and the average lift coefficient C_(La) was 0.177. Based on these computed values, the carry distance H_(S) and the duration of flight T_(S) were computed for Examples 2 to 4 as shown in Table 1. TABLE 1 Duration Duration of Carry of Flight Carry Flight Launch Distance (Meas- Distance (Computed) Angle (Measured) ured) (T: (Computed) (T_(s): (°) (H: Yards) Seconds) (H_(s): Yards) Seconds) Exam- 12 210 5.25 210 5.25 ple 1 Exam- 8 190 4.39 191 4.42 ple 2 Exam- 15 220 5.8 220 5.79 ple 3 Exam- 20 229 6.58 229 6.54 ple 4

As Table 1 above shows, the carry distance and the duration of flight match with high precision according to the golf ball trajectory computing system and the method of computing the trajectory of a golf ball of the present invention. Accordingly, the average drag coefficient C_(Da) and the average lift coefficient C_(La) obtained according to the present invention accurately show the trajectory characteristics of the golf ball. The trajectory of the golf ball computed based on these values coincides with high precision with the trajectory of the actually struck golf ball, as shown in FIG. 8. 

1. A golf ball trajectory computing system that computes a trajectory of a struck golf ball from when the golf ball is struck until the golf ball lands, comprising: initial trajectory measuring portion that measures an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after impact thereof; carry distance measuring portion that measures a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; duration-of-flight measuring portion that measures a duration of flight of the golf ball from impact thereof until the golf ball lands; and computing portion that computes a trajectory of the golf ball based on the measured initial velocity, the measured launch angle, and the measured backspin of the golf ball immediately after impact, and the carry distance and the duration of flight of the golf ball.
 2. The golf ball trajectory computing system according to claim 1, wherein said computing portion computes an average drag coefficient and an average lift coefficient for the golf ball during flight from the initial velocity of the golf ball, the launch angle, and the backspin rate immediately after impact, and from the carry distance and the duration of flight, and computes the trajectory of the golf ball using the computed average drag coefficient and the computed average lift coefficient.
 3. The golf ball trajectory computing system according to claim 1, wherein said computing portion computes the trajectory of the golf ball using equations of motion of the golf ball, and sets an average drag coefficient and an average lift coefficient so that the carry distance and the duration of flight computed by using the equations of motion of the golf ball match the carry distance measured by said carry distance measuring portion and the duration of flight measured by said duration-of-flight measuring portion, respectively, within a predetermined error range.
 4. A method of computing a trajectory of a golf ball, comprising: measuring an initial velocity, a launch angle, and a backspin rate of the golf ball immediately after the golf ball is struck; measuring a carry distance of the golf ball from an impact point to a landing point where the golf ball lands; measuring the duration of flight of the golf ball from impact thereof until the golf ball lands; and computing the trajectory of the golf ball based on the initial velocity, the launch angle, and the backspin rate of the golf ball immediately after impact thereof, based on the carry distance and the duration of flight.
 5. The method of computing the trajectory of a golf ball according to claim 4, wherein said computing of the trajectory of the golf ball further comprises computing an average drag coefficient and an average lift coefficient of the golf ball during flight from the initial velocity, the launch angle, and the backspin rate of the golf ball immediately after impact thereof, and from the carry distance and the duration of flight, and computing the trajectory of the golf ball using the computed average drag coefficient and the computed average lift coefficient.
 6. The method of computing the trajectory of a golf ball according to claim 5, wherein said computing of the trajectory of the golf ball further comprises: setting an initial value of the average drag coefficient and an initial value of the average lift coefficient of the golf ball during flight; finding a computed value of the carry distance and a computed value of the duration of flight of the golf ball based on the initial value of the average drag coefficient and the initial value of the average lift coefficient; comparing the computed value of the carry distance and the computed value of the duration of flight with the measured value of the carry distance and the measured value of the duration of flight, respectively; and based on results of said comparing, computing an average drag coefficient and an average lift coefficient of the golf ball during flight, so that the computed value of the carry distance and the computed value of the duration of flight of the golf ball fall within a predetermined error range with respect to the measured value of the carry distance and the measured value of the duration of flight, by adjusting at least one of the initial value of the average drag coefficient and the initial value of the average lift coefficient. 